Statistical Inference for Ergodic Diffusion Processes

By Peter C. Kiessler. 2006

459 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance

View Paper: https://www.semanticscholar.org/paper/f49bba4a731209343b02a5cd98b36dca1d58da38

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Citations in the corpus

Least squares estimator for Ornstein―Uhlenbeck processes driven by α-stable motions (2009, background): “For a more recent comprehensive discussion, we refer to [6,7] and the references therein.”
Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions (2018, background): “, [30], [14, 15, 50, 38, 54, 1, 2, 3]), comparably little is known about the in applications highly important multi-dimensional setting, particularly when b is modelled in a nonparametric or high-dimensional way.”
Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs (2012, methodology): “An incomplete list include kernel methods (e.g. [3], [22], [38]), penalized likelihood methods (e.g. [8]), and spectral approaches [2].”
Sharp adaptive estimation of the drift function for ergodic diffusions (2005, methodology): “It is proved in [27] that if the unknown drift function is k-times continuously differentiable, then the bandwidths αT = T −1/(2k+1) and νT = T −1/2 lead to a locally and globally rate-optimal estimator θ̂T (x).”
Asymptotic properties of MLE for partially observed fractional diffusion system (2010, methodology): “It is worth emphasizing that the result of Theorem 1 was obtained in the classical case H = 1 2 in [14].”
A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics (2011, methodology): “Well-known statistical techniques for parameter estimation [82] can then be applied to (25) to find α̃ and σ̃ from the detrended data; for example, by using a maximum likelihood estimator or many other possible estimators [55].”
Extinction and recurrence of multi-group SEIR epidemic (2013, background): “16 in [34], we see Xk is ergodic, and with respect to the Lebesgue measure its unique invariant measure νk has density (Akx (2)pk(x)) −1, where Ak = Mkσ 2 k exp ( −k σ2 k ) .”
Asymptotic Behavior of the Maximum Likelihood Estimator for Ergodic and Nonergodic Square-Root Diffusions (2013, background): “Nevertheless, if the error due to discretization is negligible then the statistical results obtained for the continuous time model are valid for discrete time observations too.”
Estimating discontinuous periodic signals in a time inhomogeneous diffusion (2009, background): “martingale part of η (see Jacod and Shiryaev 1987; Liptser and Shiryaev 2001; Kutoyants 2004 ).”
Parameter Estimation for the Square-Root Diffusions: Ergodic and Nonergodic Cases (2012, methodology): “This theory has been established mainly by Lipster and Shiryayev [17] and Kutoyants [15].”
Stochastic Gradient Descent in Continuous Time (2016, unknown): “Readers are referred to [10, 17, 26] for thorough reviews of classical statistical inference methods for stochastic diﬀerential equations.”
Parameter estimation for fractional Ornstein–Uhlenbeck processes (2009, background): “When Zt is the standard Brownian motion, this problem has been extensively studied (see for example [9], [10] and the references therein).”
Nonparametric drift estimation for i.i.d. paths of stochastic differential equations (2020, methodology): “Nevertheless, when practical implementation is done, the compact set is chosen equal to the random data range which contradicts the theoretical results (see, for reference books, e.g. Kutoyants, 1984, 2004, Iacus, 2008, Kessler et al. , 2012).”
Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency (2013, background): “In the past, several authors have investigated such a strong mode of convergence of estimators; see Bhansali and Papangelou [5], Chan and Ing [6], Findley and Wei [8], Inagaki and Ogata [14], Jeganathan [16, 17], Ogata and Inagaki [35], Sieders and Dzhaparidze [39] and Uchida [42], as well as Ibragi”
Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case (2005, methodology): “This might explain why the statistical theory for scalar diﬀusions is very well developed (see Kutoyants [15]), while inference problems for multidimensional diﬀusions are more involved and much less studied.”
Asymptotic statistical equivalence for scalar ergodic diffusions (2006, methodology): “Under ergodicity assumptions and for large T it is well known that the methodology developed for nonparametric regression can be used for inference on the drift function, for an overview see Taniguchi and Kakizawa (2000) for autoregressive processes and Kutoyants (2003) , Fan (2004) for difiusions.”